Given than line a is parallel to line b and that line c is parallel to line d, if m<13=(12x-22) & m<14=(9x-29), find m
<2.
a 65
b 70
c 85
d 110
a 65
b 70
c 85
d 110
1 answer:
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For this case we have the following system of equations:
We multiply the first equation by -4:
We have the following equivalent system of equations:
We add the equations:
We find the value of the variable "x":
Thus, the solution of the system is:
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ANswer:
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Let 
be any integer. Then
In other words:
(1) If is a multiple of 4, then 
.
(2) If dividing by 4 leaves a remainder of 1, then 
, since 
for some integer 
, and from (1) we know that 
(because, obviously, 
is a multiple of 4).
(3) If instead you get a remainder of 2, then
. This follows from (1) as well. 
.
(4) Finally, if you get a remainder of 3, then
.
In other words:
(1) If
(2) If dividing
(3) If instead you get a remainder of 2, then
(4) Finally, if you get a remainder of 3, then